SOLUTION: One side of triangle is one-fourth the longest side. The third side is 13 feet less than the longest side. The perimeter is 113. Find all three sides. The equation I got was 113

Algebra ->  Equations -> SOLUTION: One side of triangle is one-fourth the longest side. The third side is 13 feet less than the longest side. The perimeter is 113. Find all three sides. The equation I got was 113      Log On


   

Question 1092184: One side of triangle is one-fourth the longest side. The third side is 13
feet less than the longest side. The perimeter is 113. Find all three sides.
The equation I got was 113= 1/4 - 13 1/4 + x
Found 3 solutions by Alan3354, KMST, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
One side of triangle is one-fourth the longest side. The third side is 13
feet less than the longest side. The perimeter is 113. Find all three sides.
The equation I got was 113= 1/4 - 13 1/4 + x
------
L = longest side
----------------
P = L + L/4 + L-13 = 113
2L + L/4 = 126
9L/4 = 126
L/4 = 14
L = 56 ft.
--> 56, 14 & 43

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= length of the longest side, in feet
%281%2F4%29x=0.25x= length (in feet) of the side that is one-fourth of the longest side
x-13= 13 feet less than the length of the longest side
Addint those lengths we get the perimeter
x%2B%281%2F4%29x%2Bx-13=113
%281%2B1%2F4%2B1%29x-13=113
%289%2F4%29x=113%2B13
%289%2F4%29x=126
%284%2F9%29%2A%289%2F4%29=%284%2F9%29%2A126
x=56
%281%2F4%29x=%281%2F4%29%2A56=14
x-13=56-13=43
The sides of the triangle measure
highlight%2814feet%29 , highlight%2843feet%29 , and highlight%2856+feet%29 .

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
One side of triangle is one-fourth the longest side. The third side is 13
feet less than the longest side. The perimeter is 113. Find all three sides.
The equation I got was 113= 1/4 - 13 1/4 + x
Let the length of the shortest side be S

Then length of longest side is 4S

Third, or middle side = 4S - 13

We then get: S + 4S + 4S - 13 = 113

Continue solving for S, the shortest side

Multiply S by 4 to get the longest side 

Subtract 13 from the longest side to get the 3rd or middle side

This is the EASIEST way to solve this!